There is a sentiment shared among physicists that well posedness is a necessary condition for physical possibility. The arguments usually offered for well posedness have an epistemic flavor and thus they fall short of establishing the metaphysical claim that lack of well posedness implies physical impossibility. In this work we analyze the relationship of well posedness to prediction and confirmation as well as the notion of physical possibility and we devise three novel and independent argumentative strategies that may succeed where the usual epistemic arguments fail